A Gradient-Based Machine-Learning Inspired Inverse Modeling Approach for Characterization of Nonlinear Tissue...

Characterization of anisotropic nonlinear material properties along with fiber directions for soft tissues based on known deformations (strains) and external loads is a significant clinical goal.

A gradient-based inverse solver is developed to retrieve anisotropic nonlinear tissue properties. By directly minimizing nodal force residuals using known deformed and reference configurations, the method avoids repeated forward simulations. To represent complex, non-trivial spatial distributions, the material properties are parameterized using a multilayer perceptron (MLP) that maps spatial location to material behavior, in contrast to methods that use such networks to approximate the displacement field itself. For faster convergence, residual smoothing is performed, and the Jacobian computation is parallelized. The framework supports general constitutive laws as demonstrated by Neo-Hookean and Fung-type models.

The inverse solver is verified for a variety of cases, including spatially varying elasticity and anisotropic fiber distributions, and its applicability to complex 3D geometries is demonstrated on a bioprosthetic heart valve. The residual-only formulation leads to faster optimization iterations compared to Physics-Informed Neural Network (PINN) approaches, which involve computationally expensive updates to a displacement-approximating network. Unlike the Neo-Hookean constitutive model, the Fung model, especially with element-wise recovery of parameters, exhibits nonuniqueness, where different spatial distributions of parameters can yield similar residual levels; in contrast, fiber direction recovery remains robust across all cases.

The inverse solver is capable of recovering nonlinear material properties and fiber directions even for complex 3D problems with large deformations such as heart valves.